Application of Elastic Impedance to Model Based Inversion Data Using a Revised Formulation

The need for WRFM (well, reservoir, and facility management) with infill wells cannot be over-emphasized and has become essential for assets maturation and ullage utilization. EEI is the application of angle rotation in the conventional acoustic impedance under certain approximation. It essentially works by projecting intercept and gradient together with different angles which highlight different features. Extended Elastic Impedance (EEI) has proved to be a highly convenient framework for seismic AVO studies. EEI logs can be directly related to the petrophysical properties of interest, and seismic EEI reflectivity volumes can be obtained directly from the prestack data via linear projection in sin2 θ. In this project, we modelled the "chi" angles from the logs and applied the different chi angles to the prestack seismic dataset. This can be likened to a bandlimited seismic inversion product. The chi angles of the lithology indicators- Share Impedance (SI), MuRho and Density and the fluid indicators- Saturation, Fluid factor (FF) and LamdaRho were derived and applied on the seismic dataset for generating a 3D property distribution map. The input to the EEI inversion is the seismic angle sub-stacks of near (0-10deg), mid (10-20deg) and far (20-30deg) solving the AVA_2term Shuey AVO fitting function- intercept and gradient only. In some cases where the seismic S/N ratio in the ultra-far angle stack is high, it could be considered for the inversion and would give rise to the 3rd term- curvature, but in our case, it was considered noisy. To ensure stability of the inversion, the substacks were aligned both spectrally and on the waveforms and the seismic dataset was further post-processed. Amplitude maps generation and sculpting were done on the different EEI generated seismic volumes and the result provided insight in the lithology and fluid study at the reservoirs of interest. This has led to field life extension by several years more than design life and is helping to keep xxxkbpd-sized facility full via world class WRFM, infill drilling and growth projects. The EEI result helped in identified new leads and revalidated existing leads aiding well placement.

Summary Extended elastic impedance (EEI) is an extension of elastic impedance (EI) which is a generalization of acoustic impedance (AI) for nonzero angles of incidence and can be tuned to be proportional to reservoir properties. In this study, we estimated the P- (Vp) and S-wave velocities (Vs), P-wave to S-wave velocity ratio (Vp/Vs), and Poisson’s ratio of the Second Wall Creek Sand of the Teapot Dome field, Wyoming, USA, using the EEI inversion technique. Data used in the study include 3D prestack seismic data from the southern part of the field and four wells, selected from a large well database. Vs logs at the wells were constructed from Vp logs using the empirical relationships. The percent prediction errors for the four velocity properties are less than about 5% except for Poisson’s ratio at one well, supporting that the EEI inversion can be used in prediction of rock properties.

We present an integrated study of fracture detection by analyzing the seismic anisotropy in the 3D P-wave seismic data from Caidamu Basin in Northwest China. The study area lies on a big anticline which runs from southeast to northwest with the area around 400 km2, and each flank of the anticline develops a reverse fault. The target layer is a fractured gas reservoir at a depth of around 3 km just under the anticline. We first study the fracture characteristics from outcrop analogues, core samples and well logs. We then analyze the coherence and curvature attributes from post-stack seismic data, and azimuthal variation of amplitude and traveltime from pre-stack seismic data. After a careful and integrated analysis, we find that fractures are widespread and regularly distributed in the middle of study area along the anticline strike, and form good pathways and store space for fluid. The final results estimated using azimuthal analysis of pre-stack seismic amplitude data are consistent with results of core and log analysis at the well locations, which extended our knowledge of the fracture distribution in the reservoir.

The study aims to implement a high-resolution Extended Elastic Impedance (EEI) inversion to estimate the petrophysical properties (e.g., porosity, saturation and volume of shale) from seismic and well log data. The inversion resolves the pitfall of basic EEI inversion in inverting below-tuning seismic data. The resolution, dimensionality and absolute value of basic EEI inversion are improved by employing stochastic perturbation constrained by integrated energy spectra attribute in a Bayesian Markov Chain Monte Carlo framework. A general regression neural network (GRNN) is trained to learn and memorize the relationship between the stochastically perturbed EEI and the associated well petrophysical log data. The trained GRNN is then used to predict the petrophysical properties of any given stochastic processed EEI. The proposed inversion was successfully conducted to invert the volume of shale, porosity and water saturation of a 4.0 m thick gas sand reservoir in Sarawak Basin, Malaysia. The three petrophysical geobodies were successfully built using the discovery wells cut-off values, showing that the inverted petrophysical properties satisfactorily reconstruct the well petrophysical logs with sufficient resolution and an accurate absolute value at the well site and are laterally conformable with seismic data. Inversion provides reliable petrophysical properties prediction that potentially helps further reservoir development for the study field.

Elastic impedance (EI) inversion for partial angle stack seismic data is a key technology in seismic reservoir prediction within the oil and gas industry. EI inversion provides a consistent framework to invert partial angle stack seismic data, just as the AI inversion does for post-stack data. The commonly used EI inversion process is angle by angle. Hence, the inverted EI for different angles may be nonconforming, especially for the seismic data with a low signal-to-noise ratio. This paper proposes to simultaneously invert multiple partial angle stack seismic data to obtain EI for different angles at once. To obtain conformable EI, we used the joint sparse constraint on the reflection coefficients for different angles. Then, the objective function for simultaneous EI inversion was constructed. Next, synthetic seismic data profiles with three different angles were used to show the superiority of the proposed EI inversion method compared to the conventional method. At last, a real seismic data line was used to test the feasibility of the proposed method in practice. The inversion results of synthetic data and real data showed that it provides an effective new alternative method to estimate EI from partial stack seismic data.

Extended Elastic Impedance (EEI) has proved to be a highly convenient framework for seismic AVO studies. EEI logs can be directly related to the petrophysical properties of interest and seismic EEI reflectivity volumes can be obtained directly from the prestack data via linear projection in sin2theta. The directness of the EEI method is one of its strengths, making it unnecessary to perform intermediate steps such as examining conventional AVO attributes (e.g., intercepts and gradients). Consequently it can be difficult for those more familiar with the conventional AVO analysis to understand the parallels between the two methods. Once these parallels are understood we show how they can be exploited to provide new AVO attributes for background Vs/Vp ratio and AVO class based on the EEI seismic projection method.

ABSTRACTThe transformation of elastic impedance (EI) from partial‐angle‐stacked seismic data is a crucial technique in the domains of reservoir modelling. Conventionally, EI inversion is performed on a per‐angle basis, leading to significant discrepancies in EI values across different angles, which may not accurately represent actual conditions. When the signal‐to‐noise ratio (SNR) of seismic data is low, the inverted EI tends to be unstable, resulting in poor‐quality inversion outcomes. This research proposes a novel method that allows for enabling the derivation of EI for various angles simultaneously inverted from multiple partial angle‐stack seismic datasets in one process. The aim of simultaneous inversion is to potentially ensure consistent EI results. To obtain this aim, we utilize an advanced regularization method called the Gramian constraint. Consequently, the objective function for the simultaneous inversion of multiple EIs is developed. Results from both synthetic and field data demonstrate improved stability in EI inversion, especially for the case of low SNR.

Azimuthally variation of elastic impedances for fracture estimation

It is well known that if we are able to estimate acoustic impedance (AI) and a parameter related to shear-wave velocity from seismic data, our ability to discriminate between different lithologies and fluid phases will increase. Prestack inversion on individual CDP gathers and inverting directly for VP , VS , and density have been tested in several ways, but the estimated parameters are often poorly determined. A more robust approach is to apply poststack inversion on partial stacks. For inversion of the near-offset stack, AI can be calculated directly from well logs. However, for the far-offset stack, we need to derive an equivalent of the acoustic impedance that can be used to calibrate the non-zero-offset seismic reflectivity. Connolly (1998, 1999) derived such an equivalent—elastic impedance (EI)—and demonstrated how, by using elastic impedance logs (which requires shear-wave logs), he was able to perform well calibration and inversion of far-offset data. This article describes a new function—shear-wave elastic impedance (SEI)—for linking converted-wave stacks to wells using a linearization of the Zoeppritz equations. SEI is similar to EI but adapted to P-S converted seismic data. It can be computed from acoustic log data ( P - and S -wave velocities and density) and used for well calibration, wavelet estimation, and inversion of P-S reflectivity data leading to improved interpretability of converted wave data. (Equation 4 in Appendix 1 is the key mathematical formula in this approach to SEI). To test the SEI technique, we used a 3-D four-component (4-C) ocean-bottom cable (OBC) survey acquired in 1997 that covers approximately 10 km2 of the Statfjord Field (Rogno et al., 1999). Both P -wave and converted-wave data were 3-D prestack time-migrated. The hydrophone ( P ) and the vertical geophone ( Z ) component were summed to attenuate receiver side water-layer reverberations and both data sets ( PZ …

In the previous chapters, we have seen that time domain methods are good for denoising the seismic data with moderate noisy record. In order to separate true reflection amplitudes from the noisy seismic data, in this chapter, we discuss time slice singular spectrum analysis (TSSSA), a data adaptive signal decomposition based on SSA to alleviate such coloured and complex noise. This method is the time domain version of Cadzow filter but did not gain full attention until 2012. This method is applicable to pre-stack and post-stack data for denoising. By virtue of using seismic amplitudes corresponds to particular time (time slice) to benefit their strong correlation, the method was named as Time Slice SSA. It is a time domain method. In view of the above, in this chapter, Time Slice SSA (TSSSA) denoising algorithm was presented for denoising of 2D seismic reflection data. The first part of this chapter is devoted to provide the testing of the method on synthetic seismic data in comparison with f-x deconvolution (Canales 1984) and f-x SSA (Sacchi 2009) methods. In the second part, the method was applied to high-resolution seismic pre-stack and post data field data.

The classical elastic impedance (EI) inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution. So we have developed a more robust elastic impedance inversion based on the L1-norm misfit function, and the noise is assumed to be non-Gaussian. Meanwhile, some regularization methods including the sparse constraint regularization and elastic impedance point constraint regularization are incorporated to improve the ill-posed characteristics of the seismic inversion problem. Firstly, we create the L1-norm misfit objective function of pre-stack inversion problem based on the Bayesian scheme within the sparse constraint regularization and elastic impedance point constraint regularization. And then, we obtain more robust elastic impedances of different angles which are less sensitive to outliers in seismic data by using the IRLS strategy. Finally, we extract the P-wave and S-wave velocity and density by using the more stable parameter extraction method. Tests on synthetic data show that the P-wave and S-wave velocity and density parameters are still estimated reasonable with moderate noise. A test on the real data set shows that compared to the results of the classical elastic impedance inversion method, the estimated results using the proposed method can get better lateral continuity and more distinct show of the gas, verifying the feasibility and stability of the method.

In seismic reservoir characterization one aims to derive petrophysical properties of hydrocarbon reservoir conditioned to both available well-log and seismic reflection data. In this paper we present a new global pre-stack seismic AVO inversion methodology that inverts pre-stack seismic data directly for density, p-wave velocity, s-wave velocity and facies models. The retrieved subsurface models are able to reproduce the high vertical resolution of the well-log data with the spatial coverage of the seismic data. This new approach is based on an iterative genetic algorithm where the perturbation is done recurring to geostatistical simulation and co-simulation. The inverted facies model is an intrinsic part of the solution and represents the link between the elastic models (observed seismic) and the subsurface geology.KeywordsGeostatistical inversionAVO inversionPre-stack seismic inversionElastic models.

A fast Bayesian inversion method for 3D lithology and fluid prediction from prestack seismic data, and a corresponding feasibility analysis were developed and tested on a real data set. The objective of the inversion is to find the probabilities for different lithology-fluid classes from seismic data and geologic knowledge. The method combines stochastic rock physics relations between the elastic parameters and the different lithology-fluid classes with the results from a fast Bayesian seismic simultaneous inversion from seismic data to elastic parameters. A method for feasibility analysis predicts the expected modification of the prior probabilities to posterior probabilities for the different lithology-fluid classes. The feasibility analysis can be carried out before the seismic data are analyzed. Both the feasibility method and the seismic lithology-fluid probability inversion were applied to a prospect offshore Norway. The analysis improves the probability for gas sand from 0.1 to about 0.2–0.4 with seismic data.

PP-wave azimuthal elastic impedance (EI) data inverted from azimuthal prestack seismic reflection data can be theoretically and practically used for fluid- and fracture-property discrimination in naturally porous and fluid-saturated fractured reservoirs within the exploration seismic frequency band. From the perspective of the low-frequency Biot-Gassmann theory, Russell’s fluid indicator can be stably applied to fluid identification in hard-rock fractured reservoirs. Based on the low-frequency anisotropic poroelasticity theory, we first derive an azimuthal PP-wave reflection coefficient and an azimuthal EI equation in terms of Russell’s fluid indicator (a combination of acoustic impedances and dry-rock velocity ratio without the effect of squirt flow in the seismic frequency range) and two fracture indicators (i.e., normal and tangential fracture weaknesses). Using azimuthal differences in EI data, we then develop a three-step inversion method of EI difference versus angle and azimuth. It can be used accurately to estimate the fluid and fracture indicators and characterize the sensitive properties of saturated fractured porous reservoirs. Noisy synthetic data are used to verify the stability and robustness of the proposed hierarchical impedance inversion approach. A real data set acquired over a gas-bearing fractured reservoir is also used to obtain the sensitive indicators of the fluid and fracture properties, which agree well with the well-log data. Thus, our hierarchical inversion approach provides a more straightforward and efficient manner to characterize the porous and fluid-saturated fractured reservoirs.

Summary We develop a nonlinear iterative inversion algorithm for estimating three-dimensional (3D) reservoir parameters and initial fluid saturations jointly from pre-stack seismic data and fluid production history. The production measurements and the seismic data are synthetically generated from the output of a multi-phase fluid flow simulator. A Biot-Gassmann rock physics/fluid substitution model is used to enforce a deterministic link between the multi-phase flow parameters and the elastic properties. Iterative nonlinear optimization is used to solve the leastsquares minimization problem associated with the inversion. Fluid production measurements are sensitive to initial fluid saturations, fluid properties, porosity, and permeability. Pre-stack seismic data, on the other hand, provide good lateral and vertical control on lithology and fluid distributions. The proposed joint inversion approach, therefore, allows one to effectively integrate the best of the two measurement sets into a consistent 3D distribution of petrophysical variables and fluid saturations. Such distribution can be used for the accurate assessment of infill drilling and enhanced-oil-recovery operations. Synthetic test examples are presented with the sole objective to advance a proof of concept for the proposed joint inversion technique. The inversions require large computer resources and hence efficient numerical algorithms. We analyze the relative value of both sets of data and propose an extension of our algorithm to assimilate time-lapse 3D seismic data.